Many natural meandering rivers exhibit a systematic process of meander migration whereby the meander pattern sweeps down-valley. The sweep is accomplished by continual erosion on down-valley banks and deposition on up-valley banks. It is obvious that this process of channel shifting must give rise to a definite rate of transport of the eroded material. The present note attempts to demonstrate how inferring bed-material transport rates from maps estimates erosion volumes, and suggests some applications of the method.